电性任意各向异性且分块连续变化CSAMT三维有限元数值模拟

Three-dimensional CSAMT FEM modeling on electrical medium with arbitrary anisotropy and continuous variation

考虑地球介质电导率任意各向异性且随空间位置连续变化的情况,本文实现了直接求解电磁场的可控源音频大地电磁测深(CSAMT)三维有限元数值模拟.首先给出了电导率任意各向异性介质中CSAMT二次电场满足的控制方程及其相应变分问题,然后采用任意六面体单元对研究区域进行剖分,在网格单元中对任意各向异性电导率进行线性插值,解决了实际工作中岩矿石电导率各向异性且连续变化的情况,将变分问题转化为线性代数方程组的求解.电导率各向异性且连续变化一维模型三维有限元数值模拟结果与电导率各向异性且分层均匀渐进模型解析解结果对比验证了方法的有效性;三维地电模型电导率随位置线性变化且各向同性、主轴各向异性、方位各向异性和倾斜各向异性的数值模拟结果表明,电导率各向异性且连续变化对CSAMT视电阻率和相位数据均有明显的影响.

Considering that the conductivity of the earth medium is arbitrarily anisotropic and continuously changes with spatial position,this work makes three-dimensional CSAMT finite element numerical simulation to resolve the electromagnetic field directly.Firstly,we give the governing equation and its corresponding variational problem of CSAMT secondary electric field in an arbitrary anisotropic conductive medium.Then,the study area is divided into many elements of arbitrary hexahedral shape.In each element,the tri-line interpolation is performed for the arbitrary anisotropic conductivity parameter to simulate the arbitrary anisotropy and continuous change of rock and ore conductivity.The variational problem is transformed into solution of a linear algebraic equation set.Three-dimensional finite element numerical simulation results of an one-dimension conductivity model with anisotropy and continuous change are compared with analytical solution results of an anisotropic and layered progressive conductivity-model to verify the effectiveness of the method.Forward calculation is carried out on other three-dimensional geoelectric models,in which the electrical conductivity varies linearly with position and the medium is isotropic,principal axis anisotropic,azimuthal anisotropic and oblique anisotropic,respectively.Results show that the electrical conductivity anisotropy and continuous change have prominent influence on CSAMT apparent resistivity and phase data.